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arXiv · 0811.2260

Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert

Nicolas Templier
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Abstract

Soit $E/\BmQ$ une courbe elliptique. Soit $D<0$ un discriminant fondamental suffisamment grand. Si $E(\bar{\BmQ})$ contient des points de Heegner de discriminant $D$, ces points engendrent un sous-groupe dont le rang est supérieur à $\pabs{D}^{0.0009}$. Ce résultat est en accord avec la conjecture de Birch et Swinnerton-Dyer. --- Let $E/\BmQ$ be an elliptic curve. Let $D<0$ be a sufficiently large fundamental discriminant. If $E(\bar{\BmQ})$ contains Heegner points of discriminant $D$, these points generate a subgroup of rank greater than $\pabs{D}^{0.0009}$. This result is in agreement with the conjecture of Birch and Swinnerton-Dyer.

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Nicolas Templier. 2010-05-15. Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert. https://arxiv.org/abs/0811.2260

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